Conditional Probability for Mutually Exclusive Events
We define conditional probability as the probability of event A when another event B has already occurred. We define the conditional probability of event B when event A has already occurred as, P( B|A)
We can calculate its value as,
P(B|A) = P (A ∩ B)/P(A)…(ii)
Now if A and B are two mutually exclusive events then by using the multiplication rule P (A ∩ B) = 0 in eq (i)
P(B|A) = 0/P(A) = 0
Thus, the formula for conditional probability for mutually exclusive events is,
P (B | A) = 0
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Mutually Exclusive Events
We define mutually exclusive events as events that can never happen simultaneously, i.e. happening an event rules out the possibility of happening the other event. Suppose a cricket match between India and Pakistan can result in the winning of any one team and the loss of the other team both teams can never win the match simultaneously, i.e. if Pakistan wins the match then India definitely loses the match and if India wins the match Pakistan definitely loses the matches thus, we can say Winning of India and Winning of Pakistan both are mutually exclusive events. And occurring one event definitely rules the probability of the other event.
Let’s learn more about mutually exclusive events, their formula, the Venn diagram, and others in detail in this article.
Table of Content
- Mutually Exclusive Events Definition
- How to Calculate Mutually Exclusive Events?
- Probability of Mutually Exclusive Events OR Disjoint Events
- Mutually Exclusive Events Venn Diagram
- Mutually Exclusive Events Probability Rules
- Conditional Probability for Mutually Exclusive Events